Package nmw. October 20, 2017

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1 Version Package nmw October 20, 2017 Title Understanding Nonlinear Mixed Effects Modeling for Population Pharmacokinetics Description This shows how NONMEM(R) < software works. NONMEM's classical estimation methods like 'First Order(FO) approximation', 'First Order Conditional Estimation(FOCE)', and 'Laplacian approximation' are explained. Depends R (>= 3.0.0), numderiv ByteCompile yes License GPL-3 Copyright 2017, Kyun-Seop Bae Author Kyun-Seop Bae Maintainer Kyun-Seop Bae <k@acr.kr> URL NeedsCompilation no Repository CRAN Date :01:02 KST Date/Publication :29:17 UTC R topics documented: nmw-package CovStep EstStep InitStep Index 8 1

2 2 nmw-package nmw-package Understanding Nonlinear Mixed Effects Modeling for Population Pharmacokinetics Description Details This shows how NONMEM(R) < software works. This package explains First Order(FO) approximation method, First Order Conditional Estimation(FOCE) method, and Laplacian(LAPL) method of NONMEM software. Author(s) Kyun-Seop Bae References NONMEM Users guide Examples DataAll = Theoph colnames(dataall) = c("id", "BWT", "DOSE", "TIME", "DV") DataAll[,"ID"] = as.numeric(as.character(dataall[,"id"])) ntheta = 3 neta = 3 neps = 2 THETAinit = c(2, 50, 0.1) OMinit = matrix(c(0.2, 0.1, 0.1, 0.1, 0.2, 0.1, 0.1, 0.1, 0.2), nrow=neta, ncol=neta) SGinit = diag(c(0.1, 0.1)) LB = rep(0, ntheta) UB = rep( , ntheta) FGD = deriv(~dose/(th2*exp(eta2))*th1*exp(eta1)/(th1*exp(eta1) - TH3*exp(ETA3))* (exp(-th3*exp(eta3)*time)-exp(-th1*exp(eta1)*time)), c("eta1","eta2","eta3"), function.arg=c("th1", "TH2", "TH3", "ETA1", "ETA2", "ETA3", "DOSE", "TIME"), func=true, hessian=(e$method == "LAPL")) H = deriv(~f + F*EPS1 + EPS2, c("eps1", "EPS2"), function.arg=c("f", "EPS1", "EPS2"), func=true) PRED = function(theta, ETA, DATAi) { FGDres = FGD(THETA[1], THETA[2], THETA[3], ETA[1], ETA[2], ETA[3], DOSE=320, DATAi[,"TIME"]) Gres = attr(fgdres, "gradient")

3 CovStep 3 Hres = attr(h(fgdres, 0, 0), "gradient") if (e$method == "LAPL") { Dres = attr(fgdres, "hessian") Res = cbind(fgdres, Gres, Hres, Dres[,1,1], Dres[,2,1], Dres[,2,2], Dres[,3,]) colnames(res) = c("f", "G1", "G2", "G3", "H1", "H2", "D11", "D21", "D22", "D31", "D32", "D33") } else { Res = cbind(fgdres, Gres, Hres) colnames(res) = c("f", "G1", "G2", "G3", "H1", "H2") } return(res) } ####### First Order Approximation Method InitStep(DataAll, THETAinit=THETAinit, OMinit=OMinit, SGinit=SGinit, ntheta=ntheta, LB=LB, UB=UB, Pred=PRED, METHOD="ZERO") (EstRes = EstStep()) # 4 sec (CovRes = CovStep()) # 2 sec PostHocEta() # Using e$finalpara from EstStep() ######## First Order Conditional Estimation with Interaction Method #InitStep(DataAll, THETAinit=THETAinit, OMinit=OMinit, SGinit=SGinit, ntheta=ntheta, # LB=LB, UB=UB, Pred=PRED, METHOD="COND") #(EstRes = EstStep()) # 4.64 min #(CovRes = CovStep()) # 1.14 min #get("ebe", envir=e) ######## Laplacian Approximation with Interacton Method #InitStep(DataAll, THETAinit=THETAinit, OMinit=OMinit, SGinit=SGinit, ntheta=ntheta, # LB=LB, UB=UB, Pred=PRED, METHOD="LAPL") #(EstRes = EstStep()) # 4.53 min #(CovRes = CovStep()) # 1.09 min #get("ebe", envir=e) CovStep Covariance Step Description Usage Details It calculates standard errors and various variance matrices with the e$finalpara after estimation step. CovStep() Because EstStep uses nonlinear optimization, covariance step is separated from estimation step. It caculcates variance-covariance matrix of estimates on the original scale.

4 4 EstStep Value Time consumed time Standard Error standard error of the estimates in the order of theta, omega, and sigma Covariance Matrix of Estimates covariance matrix of estimates in the order of theta, omega, and sigma. This is inverse(r) x S x inverse(r) by default. Correlation Matrix of Estimates correlation matrix of estimates in the order of theta, omega, and sigma Inverse Covariance Matrix of Estimates inverse covariance matrix of estimates in the order of theta, omega, and sigma Eigen Values R Matrix S Matrix eigen values of covariance matrix R matrix of NONMEM, second derivative of log likelihood function with respect to esimation parameters S matrix of NONMEM, sum of individual cross-product of first derivative of log likelihood function with respect to esimation parameters Author(s) Kyun-Seop Bae <k@acr.kr> References NONMEM Users Guide See Also EstStep, InitStep Examples # Only after InitStep and EstStep #CovStep() EstStep Estimation Step Description This estimates upon the conditions with InitStep. Usage EstStep()

5 InitStep 5 Details It does not have arguments. All necessary arguments are stored in the e environment. It assumes "INTERACTION" between eta and epsilon for "COND" and "LAPL" options. The output is basically same with NONMEM output. Value Initial OFV Time Optim initial value of objective function time consumed for this step the raw output from optim function Final Estimates final estimates in the original scale Author(s) Kyun-Seop Bae <k@acr.kr> References NONMEM Users Guide See Also InitStep Examples # Only After InitStep #EstStep() InitStep Initialization Step Description It recevies parameters for the estimation and stores them into e environment. Usage InitStep(DataAll, THETAinit, OMinit, SGinit, ntheta, LB = rep(0, ntheta), UB = rep(0, ntheta), Pred, METHOD = METHOD)

6 6 InitStep Arguments DataAll THETAinit OMinit SGinit ntheta LB UB Pred METHOD Data for all subjects. It should contain columns which Pred function uses. Theta initial values Omega matrix initial values Sigma matrix initial values Number of thetas Lower bounds for theta vector Upper bounds for theta vector Prediction function name one of the estimation methods "ZERO", "COND", "LAPL" Details Value Prediction function should return not only prediction values(f or IPRED) but also G (first derivative with respect to etas) and H (first derivative of Y with respect to epsilon). For the "LAPL", prediction function should return second derivative with respect to eta also. All objective functions assume NONMEM "INTERACTION" option for "COND" and "LAPL" option. Omega matrix should be full block one. Sigma matrix should be diagonal one. This does not return values, but stores necessary values into the environment e. Author(s) Kyun-Seop Bae <k@acr.kr> References NONMEM Users Guide Examples DataAll = Theoph colnames(dataall) = c("id", "BWT", "DOSE", "TIME", "DV") DataAll[,"ID"] = as.numeric(as.character(dataall[,"id"])) ntheta = 3 neta = 3 neps = 2 THETAinit = c(2, 50, 0.1) # Initial estimate OMinit = matrix(c(0.2, 0.1, 0.1, 0.1, 0.2, 0.1, 0.1, 0.1, 0.2), nrow=neta, ncol=neta) OMinit SGinit = matrix(c(0.1, 0, 0, 0.1), nrow=neps, ncol=neps) SGinit LB = rep(0, ntheta) # Lower bound

7 InitStep 7 UB = rep( , ntheta) # Upper bound FGD = deriv(~dose/(th2*exp(eta2))*th1*exp(eta1)/(th1*exp(eta1) - TH3*exp(ETA3))* (exp(-th3*exp(eta3)*time)-exp(-th1*exp(eta1)*time)), c("eta1","eta2","eta3"), function.arg=c("th1", "TH2", "TH3", "ETA1", "ETA2", "ETA3", "DOSE", "TIME"), func=true, hessian=(e$method == "LAPL")) H = deriv(~f + F*EPS1 + EPS2, c("eps1", "EPS2"), function.arg=c("f", "EPS1", "EPS2"), func=true) PRED = function(theta, ETA, DATAi) { FGDres = FGD(THETA[1], THETA[2], THETA[3], ETA[1], ETA[2], ETA[3], DOSE=320, DATAi[,"TIME"]) Gres = attr(fgdres, "gradient") Hres = attr(h(fgdres, 0, 0), "gradient") if (e$method == "LAPL") { Dres = attr(fgdres, "hessian") Res = cbind(fgdres, Gres, Hres, Dres[,1,1], Dres[,2,1], Dres[,2,2], Dres[,3,]) colnames(res) = c("f", "G1", "G2", "G3", "H1", "H2", "D11", "D21", "D22", "D31", "D32", "D33") } else { Res = cbind(fgdres, Gres, Hres) colnames(res) = c("f", "G1", "G2", "G3", "H1", "H2") } return(res) } ######### First Order Approximation Method InitStep(DataAll, THETAinit=THETAinit, OMinit=OMinit, SGinit=SGinit, ntheta=ntheta, LB=LB, UB=UB, Pred=PRED, METHOD="ZERO") ######### First Order Conditional Estimation with Interaction Method InitStep(DataAll, THETAinit=THETAinit, OMinit=OMinit, SGinit=SGinit, ntheta=ntheta, LB=LB, UB=UB, Pred=PRED, METHOD="COND") ######### Laplacian Approximation with Interacton Method InitStep(DataAll, THETAinit=THETAinit, OMinit=OMinit, SGinit=SGinit, ntheta=ntheta, LB=LB, UB=UB, Pred=PRED, METHOD="LAPL")

8 Index Topic Covariance Step CovStep, 3 Topic Estimation Step EstStep, 4 Topic Initialization Step InitStep, 5 Topic Nonlinear Mixed Effects Modeling nmw-package, 2 Topic Population Pharmacokinetics nmw-package, 2 CovStep, 3 EstStep, 4, 4 InitStep, 4, 5, 5 nmw (nmw-package), 2 nmw-package, 2 8